74 lines
2.2 KiB
C
74 lines
2.2 KiB
C
/*=============================================================================
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This file is part of FLINT.
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FLINT is free software; you can redistribute it and/or modify
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it under the terms of the GNU General Public License as published by
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the Free Software Foundation; either version 2 of the License, or
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(at your option) any later version.
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FLINT is distributed in the hope that it will be useful,
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but WITHOUT ANY WARRANTY; without even the implied warranty of
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MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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GNU General Public License for more details.
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You should have received a copy of the GNU General Public License
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along with FLINT; if not, write to the Free Software
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Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA 02110-1301 USA
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=============================================================================*/
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/******************************************************************************
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Copyright (C) 2011 Fredrik Johansson
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******************************************************************************/
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#include "arith.h"
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void arith_bernoulli_polynomial(fmpq_poly_t poly, ulong n)
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{
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fmpz_t t;
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fmpz * den;
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slong k;
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if (n == 0)
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{
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fmpq_poly_set_ui(poly, UWORD(1));
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return;
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}
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fmpq_poly_fit_length(poly, n + 1);
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fmpz_init(t);
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den = _fmpz_vec_init(n + 1);
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_arith_bernoulli_number_vec(poly->coeffs, den, n + 1);
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/* Multiply the odd term by binomial(n,1) = n */
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fmpz_mul_ui(poly->coeffs + 1, poly->coeffs + 1, n);
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/* Multiply even terms by binomial coefficients */
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fmpz_one(t);
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for (k = 2; k <= n; k += 2)
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{
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fmpz_mul2_uiui(t, t, n-k+1, n-k+2);
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fmpz_divexact2_uiui(t, t, k, k-1);
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fmpz_mul(poly->coeffs + k, poly->coeffs + k, t);
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}
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/* Convert to common denominator */
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arith_primorial(poly->den, n + 2);
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for (k = 0; k <= n; k++)
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{
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fmpz_mul(poly->coeffs + k, poly->coeffs+k, poly->den);
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fmpz_divexact(poly->coeffs + k, poly->coeffs + k, den + k);
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}
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_fmpz_poly_reverse(poly->coeffs, poly->coeffs, n + 1, n + 1);
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_fmpq_poly_set_length(poly, n + 1);
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fmpq_poly_canonicalise(poly);
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_fmpz_vec_clear(den, n + 1);
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fmpz_clear(t);
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}
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